The first private company to take over an NHS hospital could make a profit of £31m in the next decade in a deal that the government's spending watchdog warns would rely on unprecedented levels of savings.

Circle Healthcare, founded by former Goldman Sachs banker Ali Parsa, runs four private treatment facilities and one NHS treatment centre and took over Hinchingbrooke hospital in Huntingdon in February. Before being handed over to Circle, the hospital had been in trouble, losing five chief executives in as many years and building up £40m of debt.

The National Audit Office reveals that Circle has already missed its own financial target, generating a deficit of £4m by September – £2m behind where Circle said it would be. The company admitted that on current projections it would end up bearing £3.5m in losses this year, which it would fund.

The report warns that "Circle's projected savings of £311m over 10 years are unprecedented as a percentage of annual turnover in the NHS... Circle's bid did not fully specify how it would achieve these savings."

The NAO says Circle stands to make £31m if it meets its targets – but only after the company had paid off the hospital's £40m debt. Unions claim that Circle's deal was an "experiment, and a dangerous one at that", saying that it was making money by cutting staff.

Christina McAnea, Unison's head of health, said: "The savings that Circle is predicting are unprecedented and that should sound alarm bells for patients and for the services that the hospital currently provides. Contrary to what we were told at the time of the bidding process, the savings are at the expense of staff, with between 270 and 300 jobs being cut. And the hospital now has several wards lying empty."

The NAO also warns that there was confusion over how to measure success in running the hospital. It said the government, the NHS and the company could not agree "what would be a successful outcome and it is unclear how success will be measured".

"For example, some expressed a view that the cumulative deficit did not need to be repaid either fully, or partly, for the franchise to be considered a success. It is also unclear who will report progress, whether it will be reported publicly, and against which indicators."

Although the watchdog admits that the government was "reasonable to look to more radical options to turn things round" and says other hospitals are considering privatisation, it says: "We have concerns about the winning bid for the franchise because most of the projected savings occur in the later years of the contract, and about how the risks associated with this were taken into account in the contract award decision."

The company said it would lose money on the hospital this year but pointed out that it was improving services and patient care. It said: "For the first year since CQC inspections began, Hinchingbrooke received a completely clean bill of health and glowing report following an unannounced inspection in August this year."

Parsa said: "Hinchingbrooke is consistently the best A&E performer and top full service hospital out of 46 in its region, and has received unprecedented positive reports from the CQC … Having overcome the quality issues facing the hospital, we have little doubt that our partners in Hinchingbrooke will overcome the financial challenges too, and next year break-even for the first time in years."

Lord Howe, the health minister, said that patient care had improved and that "Hinchingbrooke was showing that operating franchises can be a powerful tool for turning round failing hospitals".

He went on: "Cancer and accident and emergency waiting times have significantly reduced and patients are expressing increasing satisfaction with the care and services they receive. This deal has preserved a valued local hospital — had it not been agreed, Hinchingbrooke hospital may have had to close. Circle have already outlined a plan to repay the trust's past deficit of £39m. If Circle cannot return the hospital to financial balance, they won't get a penny."

• This article was amended on 8 November 2012. The original placed Hinchingbrooke hospital in Cambridge rather than Huntingdon. This has been corrected.